On computing Schur functions and series thereof

Abstract

In this paper, we present two new algorithms for computing all Schur functions $$s_\kappa (x_1,\ldots ,x_n)$$ for partitions $$\kappa $$ such that $$|\kappa |\le N$$ . For nonnegative arguments, $$x_1,\ldots ,x_n$$ , both algorithms are subtraction-free and thus each Schur function is computed to high relative accuracy in floating point arithmetic. The cost of each algorithm per Schur function is $$\mathscr {O}(n^2)$$ .